Answers
Referring to my photo, x is the length of the ladder.
Set up a trigonometric ratio to determine x
sin(71) = 28/x
Isolate x:
Multiply both side of the equation by x
sin(71)x = 28
Divide both sides by sin(71)
x = 28/sin(71)
Input into a calculator,
Which will get you the answer of
29.61
Related Questions
What is the length of the missing side of the quadrilateral shown if the perimeter is 5x+3 and 8x-4 and 10x+7
Answers
The length of the missing side of the quadrilateral shown if the perimeter is 5x+3 and sides are 8x-4 and 10x+7 and 3x+6 is -16x+12.
What is Perimeter?This is defined as the total distance around the shape.
The perimeter is the sum of the 4 sides.
Adding , 8x-4 and 10x+7 and 3x+6 , we have:
8x-4 + 10x+7 + 3x+6 = 21x+9
Subtract that from the given perimeter to get the missing side length which is:
5x+3 - 21x+9 = -16x+12
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What is the formula for AFC?
Answers
The formula for Average Fixed Cost (AFC) is: AFC = FC / Q. Where FC represents the total fixed costs incurred by a firm and Q represents the quantity of output produced by the firm.
AFC is a per-unit measure of the fixed cost of production, and represents the amount of fixed cost that is attributed to each unit of output. As the quantity of output increases, the AFC decreases, since the fixed costs are spread out over a larger number of units. AFC is an important concept in economics and business, as it is used to calculate other cost measures such as average total cost and average variable cost.
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I withdraw £80 from my savings account to go shopping.
• I spend 40% of my money in the bookshop.
• I then spend one third of the money I have left at the supermarket.
• Finally, I spend £8 on stationery.
What fraction of the £80 do I have left?
Give your answer in its simplest form.
Answers
The fraction of the £80 that you have left is 3/10.
The FractionLet's start by calculating how much money you spent at the bookshop.
40% of £80 = 0.4 x £80 = £32
So you spent £32 at the bookshop, and you now have:£80 - £32 = £48
Next, you spent one third of the money you had left at the supermarket.One third of £48 = £16
So you spent £16 at the supermarket, and you now have:£48 - £16 = £32
Finally, you spent £8 on stationery, so you now have:£32 - £8 = £24
Therefore, you have £24 left out of the original £80. To find the fraction of the £80 that you have left, we can express this as a fraction:£24 is the same as 24/80 when expressed as a fraction.
This fraction can be simplified by dividing both the numerator and denominator by 8:24/80 = 3/10
So the fraction of the £80 that you have left is 3/10. This is the simplest form.
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if f is differentiable at a must f be continuous at aa. No. If f is differetiable at a, then f is not continuous at a. The contrapositive of this statement therefore states, if f is continuous at a, then f is not differentiable at a.b. Yes. If f is differentiable at a, then f is continuous at a. the contrapositive of this statement therefore states, if f is continuous at a, then f is differentiable at a.c. No. If f is continuous at a, it is not necessarily true that the limit that defines f' exists at a.d. Yes. if f continuous at a, it is necessarily true that the limit that defines f' exists at a.
Answers
The statement "If f is differentiable at a, then f is continuous at a" is true, but "If f is continuous at a, then f is differentiable at a" is false.
Differentiability and continuity are two important concepts in calculus. A function is said to be continuous at a point if the values of the function approach a finite limit as the independent variable approaches the same value. In other words, there are no sudden jumps or breaks in the function at that point.
On the other hand, a function is said to be differentiable at a point if the limit of the rate of change of the function exists as the independent variable approaches the same value. This rate of change is called the derivative of the function and it is used to determine the slope of the function at that point.
So, it is true that if a function is differentiable at a point, then it is also continuous at that point. In other words, a continuous function must be differentiable. However, the reverse is not necessarily true. A function can reach a point where it is continuous but not differentiable. For example, the absolute value function is continuous everywhere but it is not differentiable at x = 0.
Therefore, we can say that if f is differentiable at a, then f is continuous at a. But if f is continuous at a, it does not imply that f is differentiable at a.
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I understand this concept a little I just dont know how to do it with 3 different sections
Answers
Answer:
31) -$1.25
32) $0.50
Step-by-step explanation:
Problem 31
[tex]E(X)=\frac{1}{4}(-5)+\frac{1}{4}(-20)+\frac{1}{2}(10)=-\frac{5}{4}-5+5=-\frac{5}{4}=-1.25[/tex]
Hence, this person would expect to gain -$1.25 (or lose $1.25) if they play this game.
Problem 32
[tex]E(X)=\frac{1}{4}(2)+\frac{1}{4}(20)+\frac{1}{2}(-10)=\frac{1}{2}+5-5=\frac{1}{2}=0.50[/tex]
Hence, this person would expect to gain $0.50 if they play this game.
Answer:
31. -$1.25
32. $0.50
Step-by-step explanation:
The expected value is the sum of the product of each probability and its corresponding winnings or loss.
31.
p(win $10) = 1/2
amount of winnings = $10
p(loose $5) = 1/4
amount of loss = $5
p(loose $20) = 1/4
amount of loss = $20
expected value = (1/2)($10) + (1/4)(-$5) + (1/4)(-$20)
expected value = -$1.25
32.
p(win $2) = 1/4
amount of winnings = $2
p(win $20) = 1/4
amount of winnings = $20
p(loose $10) = 1/2
amount of loss = $10
expected value = (1/4)($2) + (1/4)($20) + (1/2)(-$10)
expected value = $0.50
it take 5 hours to bake 12 loaves of bread. How long will it take to bake 15 loaves?
Answers
Answer:
= 6.25 hours.
Step-by-step explanation:
If 5 hours = 12 loaves of bread
than ? = 15 loaves of bread.
therefore 15/12 × 5 hours
= 75/12
= 6. 25 hours.
I dont seem to understand this problem can anyone help?
Answers
The time it will take to do all the activities at the same time is given as follows:
60 minutes = one hour.
How to obtain the period?Considering periodic events, they will repeat on the same day for the least common factor of the periods of each event.
The periods of each event are given as follows:
Scones: 15 minutes.Muffins: 12 minutes.Cookies: 10 minutes.
The least common factor is obtaining factoring these numbers according to their prime factors, as follows:
15 - 12 - 10|2
15 - 6 - 5|2
15 - 3 - 5|3
5 - 1 - 5|5
1 - 1 - 1
Hence:
lcm(15,12,10) = 2² x 3 x 5 = 60 minutes.
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The height of a box is 3 inches. The length is three inches more than the width. Find the width if the volume is 264.
Answers
The width of the rectangular box is W = 8 inches
What is the Volume of a Rectangle?The volume of the rectangle is given by the product of the length of the rectangle and the width of the rectangle and the height of the rectangle
Volume of Rectangle = Length x Width x Height
Volume of Rectangle = Area of Rectangle x Height
Given data ,
Let the volume of the rectangular box be V = 264 inches³
Let the height of the rectangular box be H = 3 inches
Let the length of the rectangular box be L
Let the width of the rectangular box be W
Now , L = 3 + W
And , Volume of Rectangle = Length x Width x Height
Substituting the values in the equation , we get
264 = 3 x ( W ) x ( 3 + W )
On simplifying the equation , we get
Divide by 3 on both sides of the equation , we get
3W + W² = 88
Subtracting 88 on both sides of the equation , we get
W² + 3W - 88 = 0 be equation (1)
On factorizing the equation , we get
W² + 11W - 8W - 88 = 0
Taking the common factors of the equation , we get
W ( W + 11 ) - 8 ( W + 11 ) = 0
On further simplification , we get
( W - 8 ) ( W + 11 ) = 0
The width cannot be negative , so
( W - 8 ) = 0
Adding 8 on both sides , we get
W = 8 inches
Hence , the width of the rectangular box is 8 inches
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30 points to whoever can help!!
Answers
Answer:
200
Step-by-step explanation:
9% of 200 =
200 x 0.9 =
18
What is 11 in Binary?
Answers
The binary representation of 11 is 1011. To convert decimal to binary, divide the decimal number by 2, taking the remainder at each step and concatenating the remainders in reverse order.
To convert decimal (base 10) to binary (base 2), you can divide the decimal number by 2, repeatedly taking the remainder at each step. The binary representation is obtained by concatenating the remainders in reverse order.
Here's how the conversion works for 11:
11 divided by 2 gives a quotient of 5 and a remainder of 1.
5 divided by 2 gives a quotient of 2 and a remainder of 1.
2 divided by 2 gives a quotient of 1 and a remainder of 0.
1 divided by 2 gives a quotient of 0 and a remainder of 1.
Reading the remainders in reverse order (from the last division to the first), we get 1011, which is the binary representation of 11.
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ΔLMN ≅ ΔRST, ∠L = 49º, ∠M = 10x, ∠S = 70º, and ∠T = 4y + 9.
Answers
The value of x and y in the given congruent triangles, are 7 and 13
What are congruent triangles?The triangles which share congruent corresponding angles and sides are called congruent triangles.
Given that, Δ LMN ≅ Δ RST, ∠L = 49º, ∠M = 10x, ∠S = 70º, and ∠T = 4y + 9, we need to find the x and d,
Since, we know that, the congruent triangles have congruent corresponding angles.
Here, the congruent triangles are :
∠ L = ∠ R
∠ M = ∠ S
∠ N = ∠ T
We know that, the sum of angles of a triangle is 180°,
∠ R + ∠ S + ∠ T = 180°
∠ R + 70º + 4y + 9 = 180°
49º + 70º + 4y + 9 = 180°
128º + 4y = 180º
4y = 52º
y = 13º
∵
∠ M = ∠ S
10x = 70º
x = 7
Hence, the value of x and y in the given congruent triangles, are 7 and 13
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Magdalena creates the scale drawing shown of a rectangular field. What is the area, in square meters ( m2 ), of the actual field? pls help…
Answers
The perimeter of the actual field is 91.8 meters.
The area of the actual field is 437.4 square meters.
What is the perimeter of the rectangle?The perimeter of a rectangle is defined as the addition of the lengths of the rectangle's four sides.
The perimeter of a rectangle = 2(L+W)
Where W is the width of the rectangle and L is the length of the rectangle
The scale of a rectangular field is given in the question, as follows:
1 cm = 4.5 m
So, the dimensions of the actual field, are as:
L = 7.2 × 4.5 = 32.4 m
W = 3 × 4.5 = 13.5 m
The perimeter of the actual field = 2(L+W)
The perimeter of the actual field = 2(32.4 + 13.5) = 2(45.9) = 91.8 m
The area of the actual field = L × W
The area of the actual field = 32.4 × 13.5 = 437.4 m²
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el... The vertices of parallelogram HIJK are H(0, -1), I(2, 3), J(7, -1), K(5, -5). Determine if HIJK is a parallelogram.
Answers
The correct option is, No, because HI and JK do NOT have the same slope and HK and IJ have the same slope
What are the properties of parallelogram ?Opposite sides are parallel: The pairs of opposite sides of a parallelogram are always parallel to each other.
Opposite sides are equal in length: The pairs of opposite sides of a parallelogram are equal in length.
Consecutive angles are supplementary: The consecutive angles of a parallelogram are always supplementary, meaning that they add up to 180 degrees.
Diagonals bisect each other: The diagonals of a parallelogram bisect each other, meaning that they intersect at the midpoint of each other.
The sum of the interior angles is 360 degrees: The sum of the interior angles of a parallelogram is 360 degrees.
No, because HI and JK do NOT have the same slope and HK and IJ have the same slope.
In order for a quadrilateral to be a parallelogram, opposite sides must be parallel, which means they have the same slope.
In this case, HI and JK do not have the same slope, and therefore, the opposite sides are not parallel.
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The complete question:
The vertices of parallelogram HUJK are H(0,-1),(2,3), J(7, -1),K(5,-5). Determine if HIJK is a parallelogram.
No, because HI and JK do NOT have the same slope and HK and IJ have the same slope
Yes, because HI and JK have the same slope and HK and IJ have the same slope
Yes, because the image is tilted
No, because HK and JI have the same slope, but HI and JK do NOT have the same slope
What is 15/16 as a decimal?
Answers
The decimal form of 15/16 is 0.9375.
To convert a fraction to a decimal, you can divide the numerator by the denominator. In this case, 15 divided by 16 equals 0.9375.
Alternatively, you can also use long division to find the decimal form of a fraction.
1. Set up the long division problem with 15 as the dividend and 16 as the divisor.
2. Since 16 does not go into 15, add a decimal point and a zero to the dividend.
3. Divide 16 into 150, which equals 9 with a remainder of 6.
4. Add another zero to the dividend and divide 16 into 60, which equals 3 with a remainder of 12.
5. Add another zero to the dividend and divide 16 into 120, which equals 7 with a remainder of 8.
6. Add another zero to the dividend and divide 16 into 80, which equals 5 with no remainder.
7. The final answer is 0.9375.
So, 15/16 as a decimal is 0.9375.
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Part I: Make It Simple
1. Which expression is equivalent to 3 (k kk)? S
A. 9k
B. 3k
C. 3k4
D. 3k³
Answers
f(x)=(x+5)3(x-9)(x-1) Determine the number of x-intercepts
Answers
Answer: The function has three x-intercepts.
Step-by-step explanation:
To find the x-intercepts of a function, we need to find the values of x for which the function equals zero.
So, to find the x-intercepts of the function:
F(x) = (x+5)^3(x-9)(x-1)
We need to solve the equation:
F(x) = 0
We can see that the function will be equal to zero when any of the factors on the right-hand side is equal to zero. Therefore, we need to solve the following four equations:
(x+5) = 0, which gives x = -5
(x-9) = 0, which gives x = 9
(x-1) = 0, which gives x = 1
(x+5)^3 = 0, which gives x = -5
The last equation, (x+5)^3 = 0, has a triple root at x = -5, since the factor (x+5) appears three times. Therefore, there are a total of three x-intercepts for the function:
x = -5 (with multiplicity 3), x = 1, and x = 9.
according to the empirical rule, what percentage of the observations in a data set that can be reasonably approximated by a normal curve lie within two standard deviations of the mean?
Answers
According to the empirical rule, the observations in a data set that can be reasonably approximated by a normal curve lie within two standard deviations of the mean is 95% .
The empirical rule, also known as the 68-95-99.7 rule or the three-sigma rule, is a statistical guideline that describes the approximate distribution of data that can be reasonably approximated by a normal curve. The rule states that:
Approximately 68% of the data falls within one standard deviation of the mean.
Approximately 95% of the data falls within two standard deviations of the mean.
Approximately 99.7% of the data falls within three standard deviations of the mean.
In other words, if a set of data is normally distributed (meaning it follows a bell-shaped curve), we can use the empirical rule to estimate the proportion of the data that falls within a certain range of values.
For example, let's say we have a data set that has a mean of 50 and a standard deviation of 10. Using the empirical rule, we can estimate that approximately:
68% of the data falls between 40 and 60 (one standard deviation from the mean)
95% of the data falls between 30 and 70 (two standard deviations from the mean)
99.7% of the data falls between 20 and 80 (three standard deviations from the mean)
It's important to note that the empirical rule is only an approximation, and it only applies to data that is approximately normally distributed. In some cases, the actual distribution
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The new price of a 450painting with a 45% markup is 470.25 true or false
Answers
Answer:
This is false.
Step-by-step explanation:
The correct answer would be 652.5
Which of the following is equal to the fraction below?
Answers
Answer:
Choice B
Step-by-step explanation:
(7/4)^11 = 471.431...
(7^11)/(4^11) = 471.431...
Which step is incorrect?
Answers
Answer:Step 2
Step-by-step explanation: Bc Im right
Which of the following is true?
√2 is a rational number.
-√16 is an irrational number.
0 is neither a rational number nor an irrational number.
O 1.3 is a rational number but not an integer.
Answers
if I'm Wrong Sorry And Have a Nice Day .
What is 20% of 350000?
Answers
Answer:
Step-by-step explanation:70000
Help me with this please
Answers
nswer:
Step-by-step explanation:
6*[tex]10^{6}[/tex]------100
x-------40
x=6*10^6*4*10/100=24*10^5(social media)
6*[tex]10^{6}[/tex]------100
y-------30
y=6*10^6*3*10/100=18*10^5(music)
6*[tex]10^{6}[/tex]------100
z-------25
z=6*10^6*25/100=15*10^5(games)
6*[tex]10^{6}[/tex]------100
f-------5
f=6*10^6*5/100=3*10^5(video)
Need ASAP. Questions are in the pictures attached! ty
Answers
The required rate of change of f(x) from x = -6 to x = 3 is f'(x) = 7.
What is the rate of change?Rate of change is defined as the change in value with rest to another value is called rate of change.
Here,
Given that,
f(x) = x² + 4x -15
Now, put x = -3
f(-3) = 9 - 12 - 15
f(-3) = -18
Now put x = 6
f(6)= 36 + 24 - 15
f(6) = 45
Since we know that, the rate of change of function is given as,
f'(x) = f'(a) - f'(b) / a -b
f'(x) =f'(6) - f'(-3) / a - b
f'(x) = 45 - (-18) / 6 -(-3)
f'(x) = 63 / 9
f'(x) = 7
Thus, the required rate of change of f(x) from x = -6 to x = 3 is f'(x) = 7.
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0600 Mountain Daylight Time is ____ Zulu/UTC/GMT.
Answers
0600 Mountain Daylight Time is equivalent to 1200 Zulu/UTC/GMT.
Mountain Daylight Time (MDT) is a time zone that is observed in several regions of North America during the summer months when Daylight Saving Time is in effect. It is 6 hours behind Coordinated Universal Time (UTC-6) during Daylight Saving Time.
Coordinated Universal Time (UTC) is the primary time standard by which the world regulates clocks and time. It is used in many scientific, technical, and military fields, as well as in international air traffic control.
Zulu time is a term used in aviation and military operations to refer to Coordinated Universal Time (UTC). The term "Zulu" is used because it is the letter "Z" in the NATO phonetic alphabet, and it is used to avoid confusion with other time zones during radio communication.
To convert 0600 Mountain Daylight Time to Zulu/UTC/GMT, you need to account for the time difference between Mountain Daylight Time (MDT) and Zulu/UTC/GMT.
During daylight saving time, Mountain Daylight Time is 6 hours behind Coordinated Universal Time (UTC-6). So, to convert 0600 MDT to UTC/GMT, you would need to add 6 hours.
Therefore, 0600 Mountain Daylight Time is equivalent to 1200 Zulu/UTC/GMT.
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choose similar polygons have areas of 128 in2 and 98 in 2. if the smaller polygon has a perimeter of 42 inches what is the perimeter of the larger polygon 
Answers
Let the smaller polygon have side lengths a and the larger polygon have side lengths b. Since the polygons are similar, the ratio of corresponding side lengths is the same as the ratio of their areas. That is:
b^2 / a^2 = 128 / 98
Simplifying this expression, we get:
b / a = √(128 / 98) = √(64 / 49) = (8 / 7)
Now we can use the fact that the perimeter of the smaller polygon is 42 inches:
4a = 42
a = 10.5
Substituting this into the ratio we found above, we get:
b = (8 / 7) * a = (8 / 7) * 10.5 = 12
Therefore, the larger polygon has a perimeter of:
4b = 4 * 12 = 48 inches.
Ms. Kelley is hiring teachers for the science department at a new high school. There are 9 biology teachers and 5 chemistry teachers to choose from. How many different ways can Ms. Kelley hire a staff that includes one teacher in each subject?
Answers
The total number of ways is 45.
What is an expression?An expression contains one or more terms with addition, subtraction, multiplication, and division.
We always combine the like terms in an expression when we simplify.
We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.
Example:
1 + 3x + 4y = 7 is an expression.
3 + 4 is an expression.
2 x 4 + 6 x 7 – 9 is an expression.
33 + 77 – 88 is an expression.
We have,
Ms. Kelley needs to hire one biology teacher and one chemistry teacher for the science department.
The number of ways to choose one biology teacher from a pool of 9
is 9.
The number of ways to choose one chemistry teacher from a pool of 5
is 5.
Now,
According to the multiplication principle of counting.
The total number of ways to hire one teacher from each subject.
= The number of ways to choose one biology teacher x The number of ways to choose one chemistry teacher.
= 9 x 5
= 45
Therefore,
The total number of ways Ms. Kelley can hire a staff that includes one teacher in each subject is 45.
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Solve the system of equations below. Show work.
2x+y=102x+y=10
3x-y=53x−y=5
Answers
The system of equations has its solution to be (3, 4)
Hwo to solve the system of equationsFrom the question, we have the following parameters that can be used in our computation:
2x + y = 10
3x - y = 5
Add the equations
So, we have
5x = 15
Divide by 5
x = 3
Recall that
2x + y = 10
So, we have
6 + y = 10
Evaluate
y = 4
Hence, the solution is (3, 4)
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The following angles are given in degrees and fractions of degrees. Rewrite them in degrees, arcminutes, and arcseconds.
A. 24.2 degrees?
B. 1.56 degrees?
C. 0.1 degrees?
D. 0.01 degrees?
Answers
The value is approximately equal to 12.0711°
Degrees-Minutes-SecondsWhile measuring angles, we use various units of measurements such as the degrees or the SI unit radians as per our convenience.
When we use the degree system, we can use the degree-minute-second or the degree decimal system as per our requirement of precision.
The angle in degree - minutes - seconds is 12°4'16"
We know that [tex]\frac{1}{60}[/tex] of a degree is minute and [tex]\frac{1}{60}[/tex] of a minute is a second.
Hence, [tex]\frac{1}{3600}[/tex] of a degree is a second.
Therefore the angle [tex]\theta[/tex] in degrees and decimal fractions of degrees will be:
[tex]\theta[/tex] = [tex]12+\frac{1}{60}[/tex] × 4 + [tex]\frac{1}{3600}[/tex] × 16
= [tex](12+\frac{1}{15}+\frac{1}{225} )[/tex]°
The value is approximately equal to 12.0711°
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The given question is incomplete, complete question is:
The angle 12 degrees 4'16" is given in degrees, arcminutes, and arcseconds. How do you rewrite them in degrees and decimal fractions of degrees?
What is the value of c?
Answers
Answer:
26.6°
Step-by-step explanation:
What is an angle?An angle is a measure of a turn, measured in degrees or °. Angles are made up of two rays, making the sides of the angle.
What types of angles are there?There are right angles (exactly 90 degrees), acute angles (less than 90 degrees), obtuse angles (more than 90 degrees), and reflex angles (more than 180 degrees).
If we know that the angle shown is a right angle, we also know that a right angle is equal to 90°. To solve for the value of c, we can use this equation:
90 - 63.4 = 26.6Therefore, the value of c is 26.6°.